Chronology for 1900 to 1910

1900Hilbert poses 23 problems at the Second International Congress of Mathematicians in Paris as a challenge for the 20th century. The problems include the continuum hypothesis, the well ordering of the real numbers, Goldbach's conjecture, the transcendence of powers of algebraic numbers, the Riemann hypothesis, the extension of "Dirichlet's principle" and many more. Many of the problems were solved during the 20th century, and each time one of the problems was solved it was a major event for mathematics.

1900Goursat begins publication of Cours d'analyse mathematique which introduces many new analysis concepts.

1900Levi-Civita and Ricci-Curbastro publish Méthodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.

1901Russell discovers "Russell's paradox" which illustrates in a simple fashion the problems inherent in naive set theory.

1906Koch publishes Une methode geometrique elementaire pour l'etude de certaines questions de la theorie des courbes plane which contains the "Koch curve". It is a continuous curve which is of infinite length and nowhere differentiable.

1907Fréchet discovers an integral representation theorem for functionals on the space of "quadratic Lebesgue integrable functions". A similar result was discovered independently by Riesz.

1907Einstein publishes his principle of equivalence, in which says that gravitational acceleration is indistinguishable from acceleration caused by mechanical forces. It is a key ingredient of general relativity. (See this History Topic.)

1907Heegaard and Dehn publish Analysis Situs which marks the beginnings of combinatorial topology.

1907Brouwer's doctoral thesis on the foundations of mathematics attacked the logical foundations of mathematics and marks the beginning of the Intuitionist School.

1908Hardy and Weinberg present a law describing how the proportions of dominant and recessive genetic traits would be propagated in a large population. This establishes the mathematical basis for population genetics.

1908Zermelo publishes Untersuchungen über die Grundlagen der Mengenlehre (Investigations on the Foundations of Set Theory). He bases set theory on seven axioms : Axiom of extensionality, Axiom of elementary sets, Axiom of separation, Power set axiom, Union axiom, Axiom of choice and Axiom of infinity. This aims to overcome the difficulties with set theory encountered by Cantor.

1908Poincaré publishes Science et méthode (Science and Method), perhaps his most famous popular work.

1910Russell and Whitehead publish the first volume of Principia Mathematica. They attempt to put the whole of mathematics on a logical foundation. They were able to provide detailed derivations of many major theorems in set theory, finite and transfinite arithmetic, and elementary measure theory. The third and final volume will appear three years later, while a fourth volume on geometry was planned but never completed.

1910Steinitz gives the first abstract definition of a field in Algebraische Theorie der Körper.